Twitter allows users to download parts of their data, see How to download your Twitter archive.
But what's not included in that data dump is the usernames/handles of the people that you follow or are following you. All you get is account IDs which is just an internal number and so a bit useless when it comes to archival.
Here's a way to get that data (you need to know how to run stuff in the terminal):
- Go to your Twitter profile in a desktop browser (Firefox or Chrome)
- Right click on page → Inspect → Network tab
- Click on the Following link (e.g. https://twitter.com/{yourusername}/following)